First, thank you in advance for any help that you can give a recent transplant from Windows to Ubuntu. I have a question that I have been seeking the answer too but I draw a blank at every turn.

I design websites, free of charge, for nonprofit organizations that are just starting and do not have the resources to hire a design firm. I am in need of a flash/swf editor and compiler. I had a program that I used with the awful previous O/S, however WINE would not run the program.

Thank you in advance for any help that you can offer. Since I do not earn a dime for doing this, I would prefer if the program was open source, however any suggestions are greatly appreciated.

Are you sure it makes sense to invest into Flash at all? Adobe is not going to release new versions of the player for Linux, it withdrew their Andriod plugin, and Flash never was and never will be supported by iOS. At the same time, all major browsers on all platforms (except old versions of IE) support SVG these days: http://caniuse.com/#search=svg

If you build sites with Flash now, in a year or two you'll find that the content does not display properly on the majority of devices your visitors use to access the site. I know what I'm talking about because I manage a site with a lot of Flash content and now I feel I'm starting to get cornered into a "flash ghetto" only accessible to some users - while those users are still a majority, the situation is only going to change to the worse.

Ubuntu has an awesome vector editor called Inkscape which supports SVG very well. This may be enough for you if all you need is simple vector graphics. For more complex stuff, such as scripting (which those Flash clones are unlikely to support fully anyway) you'll have to use SVG+JavaScript. I have to admit that the process is not as nice and intuitive as setting keyframes on the timeline in Flash and dragging the stuff around, but it's manageable.